Say that you have a box with mass "M." The base is given by vector "v" and height by "w." If you want to balance it on the corner, what should the angle between "v" and the surface be (image attached)?(adsbygoogle = window.adsbygoogle || []).push({});

I tried to write this out, but not sure if I did it correctly.

I figured the torque must be the same (v and w).

[tex]F_{\mathbf{v}}||\mathbf{v}||=F_{\mathbf{w}}||\mathbf{w}||[/tex]

I figured out that the mass exerted on each is as follows:

[tex]M_{\mathbf{v}}=M\cos{(\theta)}[/tex]

[tex]M_{\mathbf{w}}=M\sin{(\theta)}[/tex]

Solving for [tex]\theta[/tex], I came up with:

[tex]\theta=\arctan{(\frac{||\mathbf{w}||}{||\mathbf{v}||})}[/tex]

Is this correct? Does my reasoning make any sense?

Thanks.

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# Balancing a Cube on its Corner

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